Question

Suppose a sample of 80 with a sample proportion of 0.58 is taken from a

Answer 1

Answer:

99.7% confidence interval is $[0.4162,0.7437]$

Step-by-step explanation:

The formula for a confidence interval for a population proportion is $CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }$ where $\hat{p}$ is the sample proportion, $n$ is the sample size, and $z^*$ is the critical score for the desired confidence level.

We are given a sample size of $n=80$ and a sample proportion of $\hat{p}=0.58$. Our critical score for a 99.7% confidence level would be $z^*=normalcdf(0.9985,0,1)=2.9677$

Therefore, the approximate 99.7% confidence interval for the population parameter is $CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }=0.58\pm 2.9677\sqrt{\frac{0.58(1-0.58)}{80} }=[0.4162,0.7438]$

So we are 99.7% confident that the true population proportion is contained within the interval $[0.4162,0.7437]$